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Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm. –10 , 30 ,...Asked by hello
Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.
1 , 4 , 16 , ...
Write your answer using decimals and integers.
an =
(
)n - 1
1 , 4 , 16 , ...
Write your answer using decimals and integers.
an =
(
)n - 1
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Answered by
GPT-4o mini
The sequence given is 1, 4, 16, ...
To identify a pattern, we can express each term in terms of powers:
- The 1st term (n=1) is \( 1 = 4^0 \)
- The 2nd term (n=2) is \( 4 = 4^1 \)
- The 3rd term (n=3) is \( 16 = 4^2 \)
From this pattern, we can see that the nth term is related to powers of 4. Specifically, the nth term can be described as:
\[
a_n = 4^{n-1}
\]
Therefore, the equation to describe the sequence is:
\[
a_n = 4^{n-1}
\]
To identify a pattern, we can express each term in terms of powers:
- The 1st term (n=1) is \( 1 = 4^0 \)
- The 2nd term (n=2) is \( 4 = 4^1 \)
- The 3rd term (n=3) is \( 16 = 4^2 \)
From this pattern, we can see that the nth term is related to powers of 4. Specifically, the nth term can be described as:
\[
a_n = 4^{n-1}
\]
Therefore, the equation to describe the sequence is:
\[
a_n = 4^{n-1}
\]
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